TRS Standard pair #487072618

details

property	value
status	complete
benchmark	24.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	15.1687 seconds
cpu usage	40.4165
user time	39.1105
system time	1.30603
max virtual memory	3.6715704E7
max residence set size	3452948.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) AAECC Innermost [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPQMonotonicMRRProof [EQUIVALENT, 38 ms]
        (20) QDP
        (21) QDPQMonotonicMRRProof [EQUIVALENT, 34 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 59 ms]
        (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 20 ms]
        (26) QDP
        (27) UsableRulesProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QReductionProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) NonInfProof [EQUIVALENT, 45 ms]
        (32) AND
            (33) QDP
                (34) DependencyGraphProof [EQUIVALENT, 0 ms]
                (35) QDP
                (36) NonInfProof [EQUIVALENT, 0 ms]
                (37) AND
                    (38) QDP
                        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (40) TRUE
                    (41) QDP
                        (42) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (43) TRUE
            (44) QDP
                (45) DependencyGraphProof [EQUIVALENT, 0 ms]
                (46) QDP
                (47) NonInfProof [EQUIVALENT, 8 ms]
                (48) QDP
                (49) DependencyGraphProof [EQUIVALENT, 0 ms]
                (50) TRUE


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(x, y), x, y)
   cond2(true, x, y) -> cond3(gr(x, 0), x, y)
   cond2(false, x, y) -> cond4(gr(y, 0), x, y)
   cond3(true, x, y) -> cond3(gr(x, 0), p(x), y)
   cond3(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y)
   cond4(true, x, y) -> cond4(gr(y, 0), x, p(y))
   cond4(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false
   p(0) -> 0
   p(s(x)) -> x

Q is empty.

----------------------------------------

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false
   p(0) -> 0
   p(s(x)) -> x

The TRS R 2 is 
   cond1(true, x, y) -> cond2(gr(x, y), x, y)

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